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Existence and uniqueness of Cournot equilibrium: a contraction mapping approach

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  • Van Long, Ngo
  • Soubeyran, Antoine

Abstract

We provide sufficient conditions for existence and uniqueness of a Cournot equilibrium. The contraction mapping approach is used. Equilibrium is characterized in terms of marginal costs. The result is useful for applications to two-stage games, where, in the first stage, firms incur costs to manipulate their marginal costs of production. Cet article donne des conditions suffisantes pour l'existence et l'unicité de l'équilibre de Cournot. Notre résultat s'applique aux jeux de Cournot à deux étapes. Dans un premier temps, les firmes manipulent leurs coûts marginaux en choisissant un paramètre. Dans un deuxième temps, les firmes font la concurrence à la Cournot.

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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 67 (2000)
Issue (Month): 3 (June)
Pages: 345-348

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Handle: RePEc:eee:ecolet:v:67:y:2000:i:3:p:345-348

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References

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  1. Ngo Van Long & Antoine Soubeyran, 1999. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," CIRANO Working Papers 99s-13, CIRANO.
  2. Kolstad, Charles D & Mathiesen, Lars, 1987. "Necessary and Sufficient Conditions for Uniqueness of a Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 54(4), pages 681-90, October.
  3. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  4. Gaudet, G. & Salant, S., 1988. "Uniqueness Of Cournot Equilibrium: New Results From Old Methods," Papers 89-10, Michigan - Center for Research on Economic & Social Theory.
  5. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-89, October.
  6. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-48, October.
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Cited by:
  1. Pierre Fleckinger, 2007. "Collective Reputation and Market Structure: Regulating the Quality vs Quantity Trade-of," Working Papers hal-00243080, HAL.
  2. Joan Canton & Antoine Soubeyran & Hubert Stahn, 2008. "Environmental Taxation and Vertical Cournot Oligopolies: How Eco-industries Matter," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 40(3), pages 369-382, July.
  3. Seamus Hogan, 2009. "A New Sufficient Condition for Uniqueness in Continuous Games," Working Papers in Economics 09/06, University of Canterbury, Department of Economics and Finance.
  4. Long, Ngo Van & Soubeyran, Antoine, 2001. "Cost Manipulation Games in Oligopoly, with Costs of Manipulating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 505-33, May.
  5. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2011. "The empirical content of Cournot competition," Center for Economic Studies - Discussion papers ces11.11, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  6. Mason, Robin & Valentinyi, Akos, 2003. "Independence and heterogeneity in games of incomplete information," Discussion Paper Series In Economics And Econometrics 0307, Economics Division, School of Social Sciences, University of Southampton.
  7. Ngo Van Long & Antoine Soubeyran, 2002. "Selective Penalization Of Polluters: An Inf-Convolution Approach," CIRANO Working Papers 2002s-40, CIRANO.
  8. Van Long, Ngo, 2013. "The theory of contests: A unified model and review of the literature," European Journal of Political Economy, Elsevier, vol. 32(C), pages 161-181.
  9. Mason, Robin & Valentinyi, Ãkos, 2007. "The existence and uniqueness of monotone pure strategy equilibrium in Bayesian games," Discussion Paper Series In Economics And Econometrics 0710, Economics Division, School of Social Sciences, University of Southampton.
  10. Georg Götz, 2002. "Existence, Uniqueness, and Symmetry of Free-Entry Cournot Equilibrium: The Importance of Market Size and Technoligy Choice," Vienna Economics Papers 0214, University of Vienna, Department of Economics.
  11. Ngo Van Long & Antoine Soubeyran, 2001. "Emission Taxes and Standards for an Asymmetric Oligopoly," CIRANO Working Papers 2001s-07, CIRANO.
  12. Yukako Ono, 2000. "Outsourcing Business Service and the Scope of Local Markets," Working Papers 00-14, Center for Economic Studies, U.S. Census Bureau.
  13. Juan Enrique Martinez-Legaz & Antoine Soubeyran, 2003. "Learning from Errors," UFAE and IAE Working Papers 557.03, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  14. Elvio Accinelli & Edgar Carrera, 2006. "Unicidad del equilibrio de Nash-Cournot con correspondencias de mejor respuesta contractivas," Documentos de Trabajo (working papers) 1506, Department of Economics - dECON.
  15. Antoine Soubeyran & Ngo Van Long, 2000. "Permis de pollution et oligopole asymétrique," Économie et Prévision, Programme National Persée, vol. 143(2), pages 83-89.
  16. Ngo Van Long & Antoine Soubeyran, 2003. "A Theory of Favoritism under International Oligopoly," CIRANO Working Papers 2003s-15, CIRANO.

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